Finite Group Databasebeta

← C2×#24911063 #35572426

Subgroups — C2×#24911063 #35572426

Order 21248.

3246 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581790C211yesmaximal, characteristic, complemented
2C22×#14581772C211yesmaximal, characteristic
3C22×#14581768C211yesmaximal, characteristic
4C22×C4×Dic166C211yesmaximal, characteristic, complemented
5#24911063C2116yesmaximal, direct product factor
6C2×#19127635C212yesmaximal, complemented
7C2×#19127625C212yesmaximal
8C2×#19127598C212yesmaximal, complemented
9C2×#19127597C211yesmaximal, characteristic, complemented
10C2×#19127590C212yesmaximal
11C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
12C2×#391×C83C211yesmaximal, characteristic, complemented
13C23×Dic166C2211yescharacteristic
14C23×C4×D83C2211yescharacteristic
15C2×#14581790—28no—
16C2×#14581790C2218yescomplemented
17C2×#14581772—28no—
18C2×#14581772C2218yes—
19C2×#14581768—28no—
20C2×#14581768C2218yes—
21C2×C4×Dic166—28no—
22C2×C4×Dic166C2218yescomplemented
23C22×C4⋊Dic83C2212yes—
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2212yes—
26C22×Dic83⋊C4C2212yes—
27C22×Dic83⋊C4C2212yes—
28C22×Dic83⋊C4C2212yes—
29C22×Dic83⋊C4C2212yes—
30C22×(C2×D83)⋊C4C2212yes—
31C22×(C2×D83)⋊C4C2212yes—
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×C4×Dic83C2212yes—
35C22×C4×Dic83C2211yescharacteristic
36#19127635C22116yescomplemented
37#19127625C22116yes—
38#19127598C22116yescomplemented
39#19127597C2218yescomplemented
40#19127590C22116yes—
41C4×(C2×D83)⋊C4C2218yes—
42C2×C83⋊#95C2212yes—
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C23×Q8×C83C2211yescharacteristic
46C22×C4⋊C4×C83C2211yescharacteristic
47C22×C42×C83C2211yescharacteristic
48#391×C83C2218yescomplemented
49C2×#95×C83C2212yes—
50C2×#95×C83C2212yes—
51C24×D83C2311yescharacteristic
52C22×Dic166—24no—
53C22×Dic166—24no—
54C22×Dic166D418yes—
55C22×Dic166C2314yes—
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2312yes—
58C23×Dic83C2312yes—
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C22×C4×D83—24no—
62C22×C4×D83—24no—
63C22×C4×D83—24no—
64C22×C4×D83C2314yes—
65#14581790—232no—
66#14581772—232no—
67#14581768—232no—
68C4×Dic166—232no—
69C2×C4⋊Dic83—28no—
70C2×C4⋊Dic83D418yes—
71C2×C4⋊Dic83C2318yes—
72C2×C4⋊Dic83C2314yes—
73C2×Dic83⋊C4—28no—
74C2×Dic83⋊C4—28no—
75C2×Dic83⋊C4—28no—
76C2×Dic83⋊C4—28no—
77C2×Dic83⋊C4—28no—
78C2×Dic83⋊C4C2318yes—
79C2×Dic83⋊C4C2318yes—
80C2×Dic83⋊C4C2318yes—
81C2×Dic83⋊C4C2318yes—
82C2×Dic83⋊C4C2318yes—
83C2×(C2×D83)⋊C4—28no—
84C2×(C2×D83)⋊C4—28no—
85C2×(C2×D83)⋊C4—24no—
86C2×(C2×D83)⋊C4Q818yescomplemented
87C2×(C2×D83)⋊C4C2318yes—
88C2×(C2×D83)⋊C4C2318yes—
89C2×(C2×D83)⋊C4C2314yes—
90C2×(C2×D83)⋊C4C2314yes—
91C2×C4×Dic83—28no—
92C2×C4×Dic83—24no—
93C2×C4×Dic83C2318yes—
94C2×C4×Dic83C2314yes—
95C83⋊#95C2318yes—
96C83⋊#95C2314yes—
97C83⋊#95C2314yes—
98C22×Q8×C83—24no—
99C22×Q8×C83—24no—
100C22×Q8×C83—24no—
101C22×Q8×C83C2314yes—
102C23×C4×C83C2311yescharacteristic
103C23×C4×C83C2312yes—
104C23×C4×C83C2312yes—
105C23×C4×C83C2311yescharacteristic
106C23×C4×C83C2311yescharacteristic
107C2×C4⋊C4×C83—24no—
108C2×C4⋊C4×C83C2314yes—
109C2×C42×C83—24no—
110C2×C42×C83C2314yes—
111#95×C83C2318yes—
112#95×C83C2318yes—
113C23×D83—22no—
114C23×D83—22no—
115C23×D83—22no—
116C23×D83—22no—
117C23×D83—22no—
118C23×D83—22no—
119C23×D83C2×Q814yes—
120C23×D83C2412yes—
121C2×Dic166—232no—
122C2×Dic166—28no—
123C2×Dic166—28no—
124C2×Dic166C2×D4116yes—
125C22×Dic83—24no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83—24no—
129C22×Dic83—24no—
130C22×Dic83—22no—
131C22×Dic83—24no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83C2×D418yes—
137C22×Dic83C2×D418yes—
138C22×Dic83C2×Q814yes—
139C22×Dic83#4114yes—
140C22×Dic83C2412yes—
141C22×Dic83C2414yes—
142C22×Dic83C2414yes—
143C22×Dic83C2412yes—
144C22×Dic83C2412yes—
145C2×C4×D83—28no—
146C2×C4×D83—28no—
147C2×C4×D83—28no—
148C2×C4×D83—416no—
149C4⋊Dic83—216no—
150C4⋊Dic83C2×D4116yes—
151Dic83⋊C4—216no—
152Dic83⋊C4—216no—
153Dic83⋊C4—216no—
154Dic83⋊C4—216no—
155Dic83⋊C4—216no—
156(C2×D83)⋊C4—216no—
157(C2×D83)⋊C4—216no—
158(C2×D83)⋊C4—28no—
159(C2×D83)⋊C4C2×Q8116yescomplemented
160C4×Dic83—28no—
161C4×Dic83—216no—
162C24×C83C2411yescharacteristic
163C2×Q8×C83—28no—
164C2×Q8×C83—28no—
165C2×Q8×C83—28no—
166C2×Q8×C83—416no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—24no—
171C22×C4×C83—24no—
172C22×C4×C83—24no—
173C22×C4×C83—24no—
174C22×C4×C83—22no—
175C22×C4×C83—24no—
176C22×C4×C83—24no—
177C22×C4×C83—22no—
178C22×C4×C83C2×D414yes—
179C22×C4×C83C2×D414yes—
180C22×C4×C83C2×Q814yes—
181C22×C4×C83#4114yes—
182C22×C4×C83C2412yes—
183C22×C4×C83C2414yes—
184C22×C4×C83C2414yes—
185C22×C4×C83C2412yes—
186C22×C4×C83C2412yes—
187C4⋊C4×C83—28no—
188C42×C83—28no—
189C23×C83C22×D412yes—
190C23×C83C22×D412yes—
191C23×C83C22×Q812yes—
192C23×C83C2×#4112yes—
193C23×C83C2×#4112yes—
194C23×C832−1+412yes—
195C23×C832−1+412yes—
196C23×C83C2511yescharacteristic
197C22×D83—28no—
198C22×D83—28no—
199C22×D83—28no—
200C22×D83—22no—
201C22×D83—22no—
202C22×D83—22no—
203C22×D83—22no—
204C22×D83—22no—
205C22×D83—22no—
206C22×D83—44no—
207C22×D83—44no—
208C22×D83—44no—
209C22×D83—44no—
210C22×D83C22×Q814yes—
211Q8×C83—416no—
212C2×C4×C83—28no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—24no—
217C2×C4×C83—24no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—22no—
221C2×C4×C83—24no—
222C2×C4×C83—24no—
223C2×C4×C83—22no—
224C2×C4×C83—48no—
225C2×C4×C83—44no—
226C2×C4×C83—48no—
227C2×C4×C83#121116yes—
228C2×C4×C83C22×D414yes—
229C2×C4×C83C22×D414yes—
230C2×C4×C83C22×Q814yes—
231C2×C4×C83C2×#4114yes—
232C2×Dic83—216no—
233C2×Dic83—216no—
234C2×Dic83—28no—
235C2×Dic83—28no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—24no—
239C2×Dic83—24no—
240C2×Dic83—24no—
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—22no—
244C2×Dic83—22no—
245C2×Dic83—22no—
246C2×Dic83—22no—
247C2×Dic83—44no—
248C2×Dic83C22×D418yes—
249C2×Dic83C22×D418yes—
250C2×Dic83C22×Q814yes—
251C2×Dic83C2×#4114yes—
252C4×D83—416no—
253Dic166—232no—
254C22×C83C2×#12114yes—
255C22×C83#53314yes—
256C22×C83#54114yes—
257C22×C83#54714yes—
258C22×C83#54814yes—
259C22×C83D4×Q814yes—
260C22×C83D4×Q814yes—
261C22×C83C23×D411yescharacteristic
262C22×C83C23×D411yescharacteristic
263C22×C83C23×Q811yescharacteristic
264C22×C83C22×#4111yescharacteristic
265C22×C83C22×#4111yescharacteristic
266C22×C83C2×2−1+411yescharacteristic
267C22×C83C2×2−1+411yescharacteristic
268C2×D83—24no—
269C2×D83—24no—
270C2×D83—24no—
271C2×D83—42no—
272C2×D83—416no—
273C2×D83—42no—
274C2×D83—42no—
275C2×D83—42no—
276C4×C83—24no—
277C4×C83—44no—
278C4×C83—42no—
279C4×C83—44no—
280C4×C83C2×#12118yes—
281Dic83—28no—
282Dic83—28no—
283Dic83—24no—
284Dic83—24no—
285Dic83—42no—
286C2×#2429—831nomaximal, Sylow
287C2×C83#242918yescomplemented
288C2×C83C22×#12111yescharacteristic
289C2×C83C2×#53311yescharacteristic
290C2×C83C2×#54111yescharacteristic
291C2×C83C2×#54711yescharacteristic
292C2×C83C2×#54811yescharacteristic
293C2×C83C2×D4×Q811yescharacteristic
294C2×C83C2×D4×Q811yescharacteristic
295D83—44no—
296C22×C4⋊Q8—831no—
297C22×C22⋊Q8—831no—
298C22×C22⋊Q8—831no—
299C22×C4×Q8—831no—
300#2429—8316no—
301C2×#398—832no—
302C2×#396—832no—
303C2×#391D8311yescharacteristic, complemented
304C2×#389—832no—
305C2×#389—831no—
306C2×#388—832no—
307C2×C4×C22⋊C4—831no—
308C83C2×#242911yescharacteristic, complemented, Sylow
309C23×Q8—831no—
310C23×Q8C2×D8311yescharacteristic
311C24×C4—831no—
312C2×C4⋊Q8—838no—
313C2×C4⋊Q8—1668no—
314C2×C22⋊Q8—838no—
315C2×C22⋊Q8—838no—
316C2×C22⋊Q8—1668no—
317C2×C22⋊Q8—1668no—
318C2×C4×Q8—838no—
319C2×C4×Q8—1668no—
320C22×C4⋊C4—831no—
321C22×C4⋊C4—832no—
322C22×C4⋊C4—832no—
323C22×C4⋊C4—832no—
324C22×C4⋊C4—832no—
325C22×C4⋊C4—832no—
326C22×C4⋊C4—832no—
327C22×C4⋊C4C2×D8311yescharacteristic
328C22×C22⋊C4—831no—
329C22×C22⋊C4—831no—
330C22×C22⋊C4—832no—
331C22×C22⋊C4—832no—
332C22×C42—832no—
333C22×C42—831no—
334C22×C42C2×D8311yescharacteristic
335#398—8316no—
336#396—8316no—
337#391C2×D8318yescomplemented
338#389—838no—
339#389—8316no—
340#388—8316no—
341C4×C22⋊C4—838no—
342C2×#95—831no—
343C2×#95—832no—
344C2×#95—831no—
345C2×#95C2×D8312yes—
346C2×#95C2×D8312yes—
347C25—831no—
348C22×Q8—24no—
349C22×Q8—24no—
350C22×Q8—24no—
351C22×Q8—838no—
352C22×Q8—834no—
353C22×Q8—1664no—
354C22×Q8—1664no—
355C22×Q8C22×D8314yes—
356C23×C4—832no—
357C23×C4—832no—
358C23×C4—831no—
359C23×C4—831no—
360C23×C4—831no—
361C23×C4—834no—
362C23×C4—1664no—
363C23×C4—1664no—
364C23×C4—1664no—
365C23×C4C22×D8312yes—
366C23×C4C22×D8312yes—
367C23×C4C22×D8311yescharacteristic
368C23×C4C22×D8311yescharacteristic
369C23×C4C22×D8311yescharacteristic
370C4⋊Q8—16632no—
371C22⋊Q8—16632no—
372C22⋊Q8—16632no—
373C4×Q8—16632no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—838no—
376C2×C4⋊C4—834no—
377C2×C4⋊C4—838no—
378C2×C4⋊C4—838no—
379C2×C4⋊C4—838no—
380C2×C4⋊C4—838no—
381C2×C4⋊C4—838no—
382C2×C4⋊C4—838no—
383C2×C4⋊C4—1668no—
384C2×C4⋊C4—1668no—
385C2×C4⋊C4—1668no—
386C2×C4⋊C4—1668no—
387C2×C4⋊C4—1668no—
388C2×C4⋊C4—1668no—
389C2×C4⋊C4C22×D8314yes—
390C2×C22⋊C4—838no—
391C2×C22⋊C4—834no—
392C2×C22⋊C4—838no—
393C2×C22⋊C4—838no—
394C2×C22⋊C4—834no—
395C2×C22⋊C4—1668no—
396C2×C22⋊C4—1668no—
397C2×C22⋊C4—1664no—
398C2×C42—24no—
399C2×C42—838no—
400C2×C42—834no—
401C2×C42—1668no—
402C2×C42—1664no—
403C2×C42C22×D8314yes—
404#95—834no—
405#95—834no—
406#95—838no—
407#95C22×D8318yes—
408#95C22×D8318yes—
409C24—834no—
410C24—832no—
411C24—1662no—
412C24—1662no—
413C24—1662no—
414C24—1662no—
415C24—1662no—
416C24—1662no—
417C24C23×D8311yescharacteristic
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—416no—
422C2×Q8—8316no—
423C2×Q8—16632no—
424C2×Q8—1668no—
425C2×Q8—1668no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—33216no—
438C22×C4—838no—
439C22×C4—838no—
440C22×C4—834no—
441C22×C4—834no—
442C22×C4—832no—
443C22×C4—834no—
444C22×C4—832no—
445C22×C4—834no—
446C22×C4—832no—
447C22×C4—1662no—
448C22×C4—1662no—
449C22×C4—1662no—
450C22×C4—1668no—
451C22×C4—1668no—
452C22×C4—1668no—
453C22×C4—1662no—
454C22×C4—1662no—
455C22×C4—1664no—
456C22×C4—1664no—
457C22×C4—1664no—
458C22×C4—1662no—
459C22×C4—1664no—
460C22×C4—1662no—
461C22×C4D4×D8314yes—
462C22×C4D4×D8314yes—
463C22×C4Q8×D8314yes—
464C22×C4#1305059014yes—
465C22×C4C23×D8312yes—
466C22×C4C23×D8314yes—
467C22×C4C23×D8314yes—
468C22×C4C23×D8312yes—
469C22×C4C23×D8312yes—
470C4⋊C4—28no—
471C4⋊C4—8316no—
472C4⋊C4—16616no—
473C4⋊C4—16616no—
474C4⋊C4—16616no—
475C4⋊C4—16616no—
476C4⋊C4—16616no—
477C4⋊C4—16616no—
478C22⋊C4—8316no—
479C22⋊C4—16616no—
480C22⋊C4—16616no—
481C22⋊C4—1668no—
482C42—28no—
483C42—16616no—
484C42—1668no—
485C23—3324no—
486C23—3324no—
487C23—3324no—
488C23—3324no—
489C23—834no—
490C23—1668no—
491C23—1668no—
492C23—1668no—
493C23—1662no—
494C23—1662no—
495C23—1662no—
496C23—1662no—
497C23—1662no—
498C23—1662no—
499C23C2×D4×D8312yes—
500C23C2×D4×D8312yes—
501C23C2×Q8×D8312yes—
502C23#41×D8312yes—
503C23C2×#1305059012yes—
504C23#1458183912yes—
505C23#1458184012yes—
506C23C24×D8311yescharacteristic
507Q8—416no—
508Q8—16632no—
509C2×C4—28no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—48no—
524C2×C4—3324no—
525C2×C4—33216no—
526C2×C4—838no—
527C2×C4—838no—
528C2×C4—834no—
529C2×C4—834no—
530C2×C4—1662no—
531C2×C4—1662no—
532C2×C4—1662no—
533C2×C4—16616no—
534C2×C4—1668no—
535C2×C4—1668no—
536C2×C4—16616no—
537C2×C4—1662no—
538C2×C4—1662no—
539C2×C4—1664no—
540C2×C4—1664no—
541C2×C4—1664no—
542C2×C4—1662no—
543C2×C4—1664no—
544C2×C4—1662no—
545C2×C4#14581765116yes—
546C2×C4C2×D4×D8314yes—
547C2×C4C2×D4×D8314yes—
548C2×C4C2×Q8×D8314yes—
549C2×C4C2×#1305059014yes—
550C22—3322no—
551C22—3322no—
552C22—3322no—
553C22—33216no—
554C22—3322no—
555C22—1664no—
556C22—1664no—
557C22—1664no—
558C22C2×#1458176514yes—
559C22#1912825514yes—
560C22#1912830914yes—
561C22#1912835314yes—
562C22#1912835914yes—
563C22#1912836414yes—
564C22#1912836614yes—
565C22C22×D4×D8311yescharacteristic
566C22C22×D4×D8311yescharacteristic
567C22C22×Q8×D8311yescharacteristic
568C22C2×#41×D8311yescharacteristic
569C22C22×#1305059011yescharacteristic
570C22C2×#1458183911yescharacteristic
571C22C2×#1458184011yescharacteristic
572C4—24no—
573C4—42no—
574C4—44no—
575C4—44no—
576C4—3322no—
577C4—1668no—
578C4—1664no—
579C4—1664no—
580C4—1668no—
581C4C2×#1458176518yes—
582C2—3324no—
583C2#2491106318yesdirect product factor
584C2C22×#1458176511yescharacteristic
585C2C2×#1912825511yescharacteristic
586C2C2×#1912830911yescharacteristic
587C2C2×#1912835311yescharacteristic
588C2C2×#1912835911yescharacteristic
589C2C2×#1912836411yescharacteristic
590C2C2×#1912836611yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#391×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#391D83
hypocenterC83C2×#2429
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#391

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14581790C2semidirect
4. C22×C4×Dic166C2semidirect
5. #24911063C2direct (N × H)
6. C2×#19127635C2semidirect
8. C2×#19127598C2semidirect
9. C2×#19127597C2semidirect
12. C2×#391×C83C2semidirect
16. C2×#14581790C22semidirect
22. C2×C4×Dic166C22semidirect
36. #19127635C22semidirect
38. #19127598C22semidirect
39. #19127597C22semidirect
48. #391×C83C22semidirect
86. C2×(C2×D83)⋊C4Q8semidirect
159. (C2×D83)⋊C4C2×Q8semidirect
287. C2×C83#2429semidirect
303. C2×#391D83semidirect
308. C83C2×#2429semidirect
337. #391C2×D83semidirect
583. C2#24911063direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145817902
C22×#145817722
C22×#145817682
C22×C4×Dic1662
#249110632
C2×#191276352
C2×#191276252
C2×#191275982
C2×#191275972
C2×#191275902
C2×C4×(C2×D83)⋊C42
C2×#391×C832
C2×#242983